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A monotonic property of the optimal admission control to an M/M/1 queue under periodic observations with average cost criterion

Cao, Jianhua LU and Nyberg, Christian LU (2004) In Seventeenth Nordic Teletraffic Seminar, NTS 17, Fornebu, Norway, 25-27 August 2004
Abstract
We consider the problem of admission control to an M/M/1 queue under periodic

observations with average cost criterion. The admission controller receives

the system state information every ø :th second and can accordingly adjust the

acceptance probability for customers who arrive before the next state information

update instance. For a period of ø seconds, the cost is a linear function of the

time average of customer populations and the total number of served customers

in that period. The objective is to Ønd a stationary deterministic control policy

that minimizes the long run average cost. The problem is formulated as a discrete

time Markov decision process whose... (More)
We consider the problem of admission control to an M/M/1 queue under periodic

observations with average cost criterion. The admission controller receives

the system state information every ø :th second and can accordingly adjust the

acceptance probability for customers who arrive before the next state information

update instance. For a period of ø seconds, the cost is a linear function of the

time average of customer populations and the total number of served customers

in that period. The objective is to Ønd a stationary deterministic control policy

that minimizes the long run average cost. The problem is formulated as a discrete

time Markov decision process whose states are fully observable. By taking the

control period ø to 0 or to 1, the model in question generalizes two classical

queueing control problems: the open and the closed loop admission control to an

M/M/1 queue. We show that the optimal policy is to admit customers with a

non-increasing probability with respect to the observed number of customers in

the system. Numerical examples are also given. (Less)
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Chapter in Book/Report/Conference proceeding
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published
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in
Seventeenth Nordic Teletraffic Seminar, NTS 17, Fornebu, Norway, 25-27 August 2004
publisher
Fornebu : Telenor
ISBN
82-423-0595-1
language
English
LU publication?
yes
id
190760af-4581-4493-bc5a-5a72648d1b0b (old id 532304)
date added to LUP
2007-09-13 13:20:36
date last changed
2016-04-16 10:33:26
@inproceedings{190760af-4581-4493-bc5a-5a72648d1b0b,
  abstract     = {We consider the problem of admission control to an M/M/1 queue under periodic<br/><br>
observations with average cost criterion. The admission controller receives<br/><br>
the system state information every ø :th second and can accordingly adjust the<br/><br>
acceptance probability for customers who arrive before the next state information<br/><br>
update instance. For a period of ø seconds, the cost is a linear function of the<br/><br>
time average of customer populations and the total number of served customers<br/><br>
in that period. The objective is to Ønd a stationary deterministic control policy<br/><br>
that minimizes the long run average cost. The problem is formulated as a discrete<br/><br>
time Markov decision process whose states are fully observable. By taking the<br/><br>
control period ø to 0 or to 1, the model in question generalizes two classical<br/><br>
queueing control problems: the open and the closed loop admission control to an<br/><br>
M/M/1 queue. We show that the optimal policy is to admit customers with a<br/><br>
non-increasing probability with respect to the observed number of customers in<br/><br>
the system. Numerical examples are also given.},
  author       = {Cao, Jianhua and Nyberg, Christian},
  booktitle    = {Seventeenth Nordic Teletraffic Seminar, NTS 17, Fornebu, Norway, 25-27 August 2004},
  isbn         = {82-423-0595-1},
  language     = {eng},
  publisher    = {Fornebu : Telenor},
  title        = {A monotonic property of the optimal admission control to an M/M/1 queue under periodic observations with average cost criterion},
  year         = {2004},
}